WASHINGTON—The Consumer Financial Protection Bureau has in recent months found illegal activities in mortgage and auto-loan servicing and at payday-lending companies, a sign the bureau continues to scrutinize financial companies under the Trump administration.

The CFPB provided an update on its supervision and examination activities in a report released Thursday—the first since acting Director Mick Mulvaney took over in November 2017. Mr. Mulvaney, a Trump appointee who also serves as the White House budget chief, has introduced...